Extrapolation of Charge Density: Ver. 1.0
Taisuke Ozaki, RCIS, JAIST
Let us consider an extrapolation
of
the coordinate at the th molecular dynamic or geometry
optimization step [1,2] by a linear combination
of the previous coordinates
as



(1) 
where for three is an optimum choice in many cases.
To fit well the coordinate
to the real
coordinate , we consider the minimization of
a function :



(2) 
with respect to and .
The conditions
and
leads to



(3) 
By solving the linear equation, we may have an optimum choice of
a set of . Then, it is assumed that the difference charge
density
can be extrapolated well by the
same set of coefficients as



(4) 
where
is given by the superposition of atomic
charge densities at .
Using Eq. (4) it can be possible to estimate a good input charge density
at the th step in molecular dynamic simulations or
geometry optimizations.

 1

T. A. Arias, M. C. Payne, and J. D. Joannopoulos,
Phys. Rev. B 45, 1538 (1992).
 2

D. Alfe, Comp. Phys. Commun. 118, 32 (1999).
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